An exponential function is any function of the form:
where the base=b is positive, b is not equal to 1 and x is any real number. A logarithmic function
is any function of the form: where the base=b is positive, b is not equal to 1 and x>0 .
(It is read as "log, base b, of x")
The logarithm is a new function obtained by trying to solve for x. So
means the same as . The log is equal to the exponent for the base.
You can go back and forth between: Exponential formlogarithmic form
And Example 1
Write the following in logarithmic form:
a.is the same as
b.is the same as Example 2
Write the following in exponential form:
a. is same as .
b. is same as
If you have missing values in a simple logarithmic expression can be evaluated by rewriting the expression in
exponential form using the fact that (When expressions have the same
base then the exponents must be equal.)
Example 3
Find N in each of the following:
Rewrite
9=N